Hamas legislator Salah Bardawil also told a news conference Saturday that the slain man, Mahmoud al-Mabhouh, also took a risk by informing his Gaza family by telephone at which hotel he would be staying.
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The Syria-based al-Mabhouh was found dead in a Dubai hotel Jan. 20.
Israel's Mossad spy agency has been blamed for the killing. Israeli officials have declined comment.
Dubai police have identified 11 suspects who apparently traveled to Dubai on European passports. Two Palestinians are being held in Dubai on suspicion they helped the assassins.
"The shahid al-Mabhouh called his family from Damascus and told them he was planning to visit Dubai. He booked the plane ticket and hotel room through the internet, and this was apparently one of the mistakes that allowed the enemy's technology to track him down," said the Hamas legislator, who called on the European countries whose passports were used to prosecute Mossad's commanders
Bardawil reiterated Hamas' claim that two officers belonging to the Palestinian Authority's security apparatus took part in the assassination. He said they work for a company owned by a senior member of Fatah, Palestinian President Mahmoud Abbas' movement.
The legislator said that despite the hit squad's use of European passports, Hamas holds the "Zionist Mossad" solely responsible for al-Mabhouh's death and will look to "punish those responsible."
Also on Saturday, French Prime Minister Francois Fillon condemned the assassination al-Mabhouh and called for the truth about the killing to be established.
"I do not know all the details of this issue in Dubai. I hope that light will be shone on those responsible in this assassination," Fillon said during a visit to Syria.
"France condemns assassination. Assassination is not a means of action in international relations," he added during a news conference held with his Syrian counterpart Mohammed Naji Otri.
"All assassinations, wherever they come from, whoever ordered them should be condemned," he added.
"Like the British and the Germans, we have asked the Israeli authorities for explanations, as a French passport was used in the operation. We want to know the whole truth on the issue."
Reuters and AP contributed to the report